All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
661
A is thrice as good a workman as B and takes 60 days less than B to complete a piece of work. How long will they take working together?
Answer:
22.5 days
Step 1: Time ratio A:B = 1:3. Let A take x days and B take 3x days. Step 2: The difference is 3x - x = 2x. We are given 2x = 60, so x = 30. A takes 30 days and B takes 90 days. Step 3: Total work = LCM(30, 90) = 90. Combined efficiency = 3 + 1 = 4. Time together = 90/4 = 22.5 days.
662
A is twice as good a workman as B and therefore takes 10 days less than B to finish a job. In how many days can A alone finish the job?
Answer:
10 days
Step 1: Efficiency ratio A:B = 2:1. Therefore, the time ratio is 1:2. Step 2: Let A take x days and B take 2x days. The difference is 2x - x = x days. Step 3: We are given that x = 10. Thus, A takes 10 days alone.
663
A is 50% more efficient than B. If B alone takes 30 days to finish a task, how long will A take alone?
Answer:
20 days
Step 1: Efficiency ratio of A:B is 150:100, which simplifies to 3:2. Step 2: Total work = B's efficiency * B's time = 2 * 30 = 60 units. Step 3: Time taken by A alone = Total work / A's efficiency = 60 / 3 = 20 days.
664
A is thrice as fast as B. If they complete a work together in 15 days, how many days will B take alone to finish it?
Answer:
60 days
Step 1: Efficiency ratio of A:B is 3:1. Total efficiency = 3 + 1 = 4 units/day. Step 2: Total work = 4 units/day * 15 days = 60 units. Step 3: Time taken by B alone = Total work / B's efficiency = 60 / 1 = 60 days.
665
A is twice as fast as B. Together they can finish a piece of work in 14 days. How many days will A alone take to finish the work?
Answer:
21 days
Step 1: Efficiency ratio of A:B is 2:1. Total efficiency = 2 + 1 = 3 units/day. Step 2: Total work = Combined efficiency * time = 3 * 14 = 42 units. Step 3: Time taken by A alone = Total work / A's efficiency = 42 / 2 = 21 days.
666
A, B, and C can do a work in 16, 32, and 48 days respectively. Together they will take:
Answer:
8 8/11 days
Step 1: LCM(16, 32, 48) = 96 units. Step 2: A's efficiency = 6, B's = 3, C's = 2. Step 3: Total efficiency = 6 + 3 + 2 = 11. Time = 96/11 = 8 8/11 days.
667
P, Q, and R can complete a job in 12, 24, and 36 days respectively. In how many days can they complete the job together?
Answer:
6 6/11 days
Step 1: Total work = LCM(12, 24, 36) = 72 units. Step 2: Efficiencies: P = 6, Q = 3, R = 2. Step 3: Combined efficiency = 6 + 3 + 2 = 11. Time taken = 72/11 = 6 6/11 days.
668
A can do a work in 18 days, B in 27 days, and C in 54 days. Working together, they will finish in:
Answer:
9 days
Step 1: Total work = LCM(18, 27, 54) = 54 units. Step 2: Efficiencies: A = 3, B = 2, C = 1. Step 3: Combined efficiency = 3 + 2 + 1 = 6 units/day. Time = 54/6 = 9 days.
669
X, Y, and Z can finish a work in 10, 20, and 30 days respectively. Together they will finish the work in:
Answer:
5.45 days
Step 1: LCM(10, 20, 30) = 60 units. Step 2: X's efficiency = 6, Y's = 3, Z's = 2. Step 3: Total efficiency = 6 + 3 + 2 = 11 units/day. Time taken = 60/11 = 5.45 days.
670
A, B, and C take 6, 8, and 24 days to finish a piece of work. How long will it take them to finish the work together?
Answer:
3 days
Step 1: Total work = LCM(6, 8, 24) = 24 units. Step 2: A's efficiency = 4, B's = 3, C's = 1. Step 3: Combined efficiency = 4 + 3 + 1 = 8 units/day. Time taken = 24/8 = 3 days.